One of the key components for achieving flexible, robust, adaptive and open-ended language-based communication between humans and robots – or between robots and robots – is rich deep semantics. AI has a long tradition of work in the representation of knowledge, most of it within the logical tradition. This tradition assumes that an autonomous agent is able to derive formal descriptions of the world which can then be the basis of logical inference and natural language understanding or production. This paper outlines some difficulties with this logical stance and reports alternative research on the development of an ?embodied cognitive semantics? that is grounded in the world through a robot?s sensori-motor system and is evolutionary in the sense that the conceptual frameworks underlying language are assumed to be adapted by agents in the course of dialogs and thus undergo constant change.